# Given a sequence (xn) and a real number L , prove or give a counterexample for the following statement: (xn) converges to L if and only if  (|xn − L|) converges to 0

Question

Given a sequence (xn) and a real number L , prove or give a counterexample for the following statement:

(xn) converges to L if and only if  (|xn − L|) converges to 0